Question

(х^2-4x+1)(x^2-4x+ 2) = 2

Answer 1

Ответ:

Объяснение:

пусть x²-4x+1=t, тогда

t(t+1)=2

t²+t-2=0

D= 1+8=9

t1= (-1-3)/2= -2

t2= (-1+3)/2= 1

1) x²-4x+1=-2

x²-4x+3=0

D= 16-12= 4

x1= (4-2)/2= 1

x2= (4+2)/2= 3

2) x²-4x+1=1

x(x-4)=0

x3= 0

x4= 4

Ответ: x1=1, x2= 3, x3=0, x4=4

Answer 2

(х²-4x+1)(x²-4x+2) = 2

Пусть х²-4x+1 = t, тогда

x²-4x+ 2 = x²- 4x + 1 + 1 = t+1

t*(t+1)=2

t²+t-2=0

D = 1² - 4*(-2) = 1+8 = 9 = 3²

$t_{1} =\frac{-1+3}{2*1} = \frac{2}{2} = 1$

$t_{2} =\frac{-1-3}{2*1} = -\frac{4}{2} = -2$

Вернёмся к замене:

$\left[\begin{array}{ccc}x^{2}-4x+1=1 \\x^{2}-4x+1=-2\\\end{array}$

х²-4x+1 = 1

х²-4x = 0

х*(х-4) =0

х = 0

х-4=0

х=4

х²-4x+1 = -2

х²-4x+3 = 0

D = (-4)² - 4*3 = 16-12 = 4 = 2²

$x_{1} =\frac{4+2}{2*1} = \frac{6}{2} = 3$

$x_{2} =\frac{4-2}{2*1} = \frac{2}{2} = 1$

Ответ: x = 0, x = 1, x = 3, x = 4

Answer 3

The equation you provided is a quadratic equation in terms of $x$. To solve it, we need to simplify and factor the expression on the left-hand side, then set it equal to 2:

$(x^2 - 4x + 1)(x^2 - 4x + 2) = 2$

Let's start by factoring the expression $(x^2 - 4x + 1)$ and $(x^2 - 4x + 2)$:

$x^2 - 4x + 1$ can be factored as $(x - 1)^2$. $x^2 - 4x + 2$ doesn't have simple integer factors.

So, the equation becomes:

$(x - 1)^2 \cdot (x^2 - 4x + 2) = 2$

Now, we have to solve for $x$. However, it's important to note that the equation is a bit more complicated due to the second factor $(x^2 - 4x + 2)$ not having simple integer factors. It's possible that this equation might have complex solutions.

Unfortunately, I cannot provide the exact solutions for $x$ in this equation as it involves a higher degree polynomial, and there isn't a general formula to find the roots of quartic equations (equations with degree 4) that works in all cases. To solve this equation, you might need to use numerical methods or specialized software.

If you're looking for numerical solutions, you can use methods like the Newton-Raphson method, the bisection method, or software like Mathematica, MATLAB, or Python with libraries like NumPy and SciPy to find approximate solutions.